Optimal decomposition and classification of linear mixtures of ARMA processes

We consider the problem of detecting and classifying an unkn own number of multiple simultaneous Gaussian autoregressive-moving average (ARMA) si gnals with unknown variances given a finite length observation of their sum and a dictionary of candidat e ARMA models. We introduce the concept of mixture of ARMA ( ARMA) process and show that the detection and classification prob lem is equivalent to decomposition of a ARMA process. The optimal solution in an information theoretic s ense is found by applying the minimum description length (MDL) prin c ple. Computation of the MDL solution requires the maximization of a likelihood function of the va riances of the ARMA components for a series of subsets from the dictionary. This maximization is perfor med efficiently by combining the EM algorithm with the Rauch-Tung-Striebel optimal smoother or with a Wie ner filter-based approximation thereof and a new result on subset selection. The performance of the algor ithm is illustrated by numerical simulations. Possible extensions of the method are discussed. Potential applications are in the area of sound recognition and stochastic NMR spectroscopy. Authorization to publish this abstract separately is grant ed. EDICS Classification: SP 3.7.1, SP 3.6.1, SP 3.1.1. Christophe Couvreur’s work is also supported in part by the N ational Fund for Scientific Research of Belgium (F.N.R.S.). yYoram Bresler’s work is also supported in part by a National S cience Foundation grant No. MIP 91-57377.